Abstract: Asian option is a significant financial derivative instrument, which is one of the most popular path-dependent options. Its income is decided by the average value of underly asset within the whole lifetime of the option. Influenced by the dynamic uncertainty of risk, the interest rate in foreign exchange market is assumed to be modeled by uncertain process and its law of change obeys an uncertain differential equation. In order to hedge against risks from the foreign exchange market, the bank provides a contract for investors to give them a kind of right instead of obligation to buy foreign exchange at a knock exchange rate. Naturally, for possessing such right, the investor needs to pay for the contract. Hence, based on the uncertain foreign exchange model, this paper studies the Asian option problem. Combining uncertainty theory and fair price principle, the pricing formulas of geometric average Asian option are deduced.

Key words: Asian option, uncertain process, uncertain differential equation